Let be a mixed graph and [Formula: see text] be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in , then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix [Formula: see text] of a mixed graph , where [Formula: see text] ([Formula: see text]) if [Formula: see text] is an arc of , [Formula: see text] if [Formula: see text] is an undirected edge of , and [Formula: see text] otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds on the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5334441 | PMC |
| http://dx.doi.org/10.1186/s13660-017-1329-8 | DOI Listing |
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